Chapter 4: Q35. (page 172)

Give an example of two matrices A and B whose product is commutative so that $A B = B A$

Short Answer

Expert verified

The required matrices are $A = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$ and $B = [\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix}]$

Step by step solution

Step 1- Determine the dimensions of the required matrices

The dimensions for both the matrices should be same so the dimensions $2 \times 2$ are the best choice.

– Write the matrices

Each matrix should contain 0 in place of first row and second column along with the second row and first column so write the matrices.

$A = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$ $B = [\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix}]$

Step 3- Check the matrices

Perform multiplication between the obtained matrices A and B.

$\begin{matrix} A B = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] \cdot [\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix}] \\ = [\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix}] \end{matrix}$

Now, perform multiplication between B and A.

$\begin{matrix} B A = [\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix}] \cdot [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] \\ = [\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix}] \end{matrix}$

Step 3- Make the conclusion

As the obtained matrices are satisfying the commutative property $A B = B A$ so the obtained matrices are the required matrices.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Give an example of two matrices A and B whose product is commutative so that $A B = B A$

Short Answer

Step by step solution

Step 1- Determine the dimensions of the required matrices

– Write the matrices

Step 3- Check the matrices

Step 3- Make the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

Pure Maths

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

Give an example of two matrices A and B whose product is commutative so thatAB=BA

Short Answer

Step by step solution

Step 1- Determine the dimensions of the required matrices

– Write the matrices

Step 3- Check the matrices

Step 3- Make the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

Pure Maths

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

Give an example of two matrices A and B whose product is commutative so that $A B = B A$